Gilles Mourot

Non-linear dynamic system identification : a multi-model approach

We are concerned with models which are able to describe multiple-input multiple-output (MIMO) non-linear dynamic systems. These models are represented in the form of rules and are known as Tagaki-Sugeno models. An identification algorithm for these models based on input and output data is presented. Parameter estimation is based on the calculation of model sensitivity functions with respect to their parameters. Some aspects of structure identification are also tackled, i.e. determination of local model orders and number of rules.

Structure identification in multiple model representation: elimination and merging of local models

This paper deals with the structure optimisation of a multiple model. The proposed technique assumes an initial lattice partition of the operating space of the system. The complexity of the model is optimised through an iterative procedure which includes three operations: elimination of less important local models, merging of neighbouring local models that can describe the same behaviour of the system, parameter optimisation of the resultant structure. The procedure is illustrated on a simulation example.

Parameter estimation of switching piecewise linear system

During the last years, a number of methodological papers on models with discrete parameter shifts have revived interest in the so-called regime switching models. Piecewise linear models are attractive when modelling a wide range of nonlinear system and determining simultaneously i) the data partition ii) the time instant of change iii) the parameter values of the different local models. This is a difficult problem for which no solution exists in the general case and we show here some aspects and particular results concerning the problem of off line learning of switching time series. We propose a method for identifying the parameters of the local models when choosing an adapted weighting function, this function allowing to select the data for which each local model is active. Indeed the proposed method is able to solve simultaneously the data allocation and the parameter estimation. The feasibility and the performance of the procedure is demonstrated using several academic examples.

Model structure simplification of a biological reactor

This article proposes an analytical method for decomposing a dynamic nonlinear system into a multiple model form in order to reduce its complexity and to study more easily identification, stability analysis and controller design problems. The majority of existing methods are order reduction based techniques, which come with an information loss of the initial system, whereas the method proposed here avoids this particular loss. The multiple model constitutes an efficient tool to represent nonlinear systems. These are decomposed into several linear time invariant systems (LTI) which are weighted and aggregated that allows to benefit from important analysis tools. This method is applied to a simplified activated sludge reactor model.

Fault detection and isolation with robust principal component analysis

Principal component analysis (PCA) is a powerful fault detection and isolation method. However, the classical PCA which is based on the estimation of the sample mean and covariance matrix of the data is very sensitive to outliers in the training data set. Usually robust principal component analysis was applied to remove the effect of outliers on the PCA model. In this paper, a fast two-step algorithm is proposed. First, the objective was to find a robust PCA model that could be used for outliers detection and isolation. Hence a scale-M estimator (R.A. Maronna, 2005) is used to determine a robust model. This estimator is computed using an iterative re-weighted least squares (IRWLS) procedure. This algorithm is initialized from a very simple estimate derived from a one-step weighted variance-covariance estimate (A. Ruiz-Gazen, 1996). Second, structured residuals are used for multiple fault detection and isolation. These structured residuals are based on the reconstruction principle and the existence condition of such residuals is used to determine the detectable faults and the isolable faults. The proposed scheme avoids the combinatorial explosion of faulty scenarios related to multiple faults to consider. Then, this procedure for outliers detection and isolation is successfully applied to an example with multiple faults.

Nonlinear PCA combining principal curves and RBF-networks for process monitoring

The use of principal component analysis (PCA) for process monitoring applications has attracted much attention recently. PCA is the optimal linear transformation with respect to minimizing the mean square prediction error but it only considers second order statistics. If the data have nonlinear dependencies, an important issue is to develop a technique which takes higher order statistics into account and which can eliminate dependencies not removed by PCA. Recognizing the shortcomings of PCA, a nonlinear extension of PCA is developed. The purpose of this paper is to present a nonlinear generalization of PCA (NLPCA) by combining the principal curves and RBF-Networks. The NLPCA model consists of two RBF networks where the nonlinear transformations of the input variables (that characterize the nonlinear principal component analysis) are modelled as a linear sum of radially symmetric kernel functions by using the first network. The nonlinear principal component, which represents the desired output of the first network, are obtained by the principal curves algorithm. The second network tries to perform the inverse transformation by reproducing the original data. The proposed approach is illustrated by a simulation example.

Rainfall–runoff multi-modelling for sensor fault diagnosis

Abstract In view of the limitations of flood and pollution prevention in urban sewage networks, the control of hydraulic equipment now calls for more reliable measurements provided by different sensors. The sensor fault detection and isolation described here requires the availability of a rainfall–runoff relationship in order to apply analytical redundancy-based diagnostic procedures. However, because this relationship is conspicuously non-linear and time varying, the latter relationship is identified by using a multi-model approach. The proposed modelling approach has been successfully tested on a watershed located in an urban area of Nancy, in eastern France, using actual rainfall and runoff data taken from the sewerage control centre database. The model obtained is then used to increase the degree of information redundancy in order to implement a sensor fault diagnostic procedure. Since no statistical hypothesis on measurement uncertainties can be made, interval arithmetic is used to derive residual tolerance.

Identification of switching systems using change detection technique in the subspace framework

The paper describes an identification technique of switching system. The considered system is represented as a weighted sum of local models. To estimate the switching times, a change detection technique is applied. It provides the weights associated to the local models. The Markov parameters of these models are identified by a subspace method. This calculation can yield similar local models which are merged. The procedure of parameter identification an models merging is repeated until convergence. The performance of the approach is investigated on a simulation example.

Subspace Method for Sensor Fault Detection and Isolation-Application to Grinding Circuit Monitoring

Abstract Sensor fault detection and isolation method is proposed in this paper. The method is only based on the knowledge of the input and output data. Any parameter estimation nor system order determination are necessary. The proposed technique uses matrix projection in subspace framework. The sensitivity of the method to sensor faults is shown. The method is applied for sensor fault detection and isolation in a grinding circuit.

Multi-task learning with one-class SVM

Multi-task learning technologies have been developed to be an effective way to improve the generalization performance by training multiple related tasks simultaneously. The determination of the relatedness between tasks is usually the key to the formulation of a multi-task learning method. In this paper, we make the assumption that when tasks are related to each other, usually their models are close enough, that is, their models or their model parameters are close to a certain mean function. Following this task relatedness assumption, two multi-task learning formulations based on one-class support vector machines (one-class SVM) are presented. With the help of new kernel design, both multi-task learning methods can be solved by the optimization program of a single one-class SVM. Experiments conducted on both low-dimensional nonlinear toy dataset and high-dimensional textured images show that our approaches lead to very encouraging results.